## View abstract

### Session S06 - Interacting Stochastic Systems

Tuesday, July 13, 14:00 ~ 14:35 UTC-3

## Random walk in a field of weakly killing exclusion particles

### Dirk Erhard

#### Universidade Federal da Bahia, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakfdc2b14edbbc3b408ddd987387923600').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyfdc2b14edbbc3b408ddd987387923600 = '&#101;rh&#97;rdd&#105;rk' + '&#64;'; addyfdc2b14edbbc3b408ddd987387923600 = addyfdc2b14edbbc3b408ddd987387923600 + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m'; var addy_textfdc2b14edbbc3b408ddd987387923600 = '&#101;rh&#97;rdd&#105;rk' + '&#64;' + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m';document.getElementById('cloakfdc2b14edbbc3b408ddd987387923600').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyfdc2b14edbbc3b408ddd987387923600 + '\'>'+addy_textfdc2b14edbbc3b408ddd987387923600+'<\/a>';

Consider a simple random walk, and independently of it the simple symmetric exclusion process on $\mathbb{Z}^d$. The random walk gets killed at rate epsilon when it shares a site with an exclusion particle. Using the relation to the parabolic Anderson model and the theory of regularity structures, I will present exact asymptotics for the survival probability of the random walk as epsilon tends to zero in dimension $d=3$. To establish these, precise bounds on the joint cumulants of the exclusion process are needed, which hold as soon as $d\geq 3$. I will also discuss what is missing to establish the corresponding result in $d=2$.

Joint work with Martin Hairer (Imperial College London).